I have an area 8 feet by 8 feet square. To convert to an octagon, what would the length of each side be?

Question

I am formulatically challenged. Please explain in simple terms. Thanks.

ok, so for those of you who say the answer is "4" is obviously wrong. Take a square piece of paper and fold it evenly in threes. Now unfold and re-fold the opposite direction. Open and you have 9 equal size squares. Fold each corner square in half. The diagonal folds are NOT the same length as the other sides...the diagonals are longer. I need all eight to be equal sizes. Thanks.

Answer 1

Unfortunately, the people above have misused geometry.

The way that you'd solve this in a geometry class would involved quite a bit of trigonometry. Here's a way to solve it without using as much. (I worked it out both ways and both methods give the same result. I also checked the result.)

I'm assuming that your octagon is regular.

Draw a regular octagon. Call the length of each side a.

Now use vertical and horizontal lines to draw gridlines on the octogon. This divides the octagon into four triangles, four rectangles, and a square in the middle.

The square has area a^2..

The triangles are 45-45-90 triangles having hypotenuse a. This means that both sides are a / square root of 2. This means that each triangle has area:

1/2 * (a / sqr(2)) * (a / sqr(2)) = a^2 / 4.

The rectangles have one side that is a side of the octagon (a) and one side that is a leg of the triangle (a / sqr(2)).

This means that the rectangles have area:

a * (a / sqr(2)) = a^2 / sqr(2).

The octagon's area is equal to the sum of the areas of its regions:

4 triangles + 4 rectangles + 1 square

4*(a^2 / 4) + 4*(a^2 / sqr(2)) + a^2 =

a^2 + 2sqr(2)*a^2 + a^2 =

a^2 (2 + 2sqr(2)) = 64.

Solve for a, and you get approximately 3.6407 feet.

That is to say, an octagon having a side length of 3.6407 feet has the same area as a square having a side length of 8 feet.

This seems contradictory until you realize that an regular octagon isn't made up of just squares and triangles. If they were, then the "diagonal" sides would be longer than the "horizontal" and "vertical" sides.

Answer 2

8/3's it is. Draw an 8x8 square. Divide each side into three sections. Draw diagonals to create right triangles at the corners of the square. If you were to "cut the triangles off" you would be left with a regular octagon; all sides equal.no you wouldn't, my bad! it's an octagon, but not regular!

Answer 3

Second answer is correct. If you have an 8'x8' linear square, the four sides at 8' is 4x8 equaling 32, naturally, an Octagon has eight sides so 32 divided by 8 equals 4

Answer 4

Let width= x ft Length= x+8 ft Area=84 ft^2 x(x+8)=84 x^2+8x-84=0 (x+14)(x-6)=0 x= 6, x= -14 (not possible) dimension of room= 14 ft by 6 ft

Answer 5

Easy dumbass.....an octagon will have equal sides of 4 feet each ( draw a square, now take divide each side by 2, u have 8 peices, and an octagon have 8 sides, therefore its 4 feet each )

Answer 6

an octagon has 8 sides. divide your square (w/c has four sides) by 2. now you have 8 sides at 4ft each. position the 8 sides at an angle of 45 degrees between 2 sides. you now have a perfect octagon.

Answer 7

8 devided by 3
= 2.66667

each side.

do it on simple paper in inches or cms and measure.